Toward Reliable and Insightful Entropy Calculations on Flexible Molecules

The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs-Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (CH₂, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.